ABEL ARITHMETIC FUNCTIONS IN FINITE CHARACTERISTIC

David Adam (1)

1 GAATI - Laboratoire de Géométrie Algébrique et Applications à la Théorie de l'Information

We define Abel arithmetic functions in function fields with positive characteristic. We prove that any Abel arithmetic function with exponential type lesser than [Formula: see text] is a polynomial, the bound [Formula: see text] being optimal. This provides an analog of a Bertrandias' result. Some q-analogs are considered too.

Domaines: Géométrie algébrique [math.AG]

David Adam. ABEL ARITHMETIC FUNCTIONS IN FINITE CHARACTERISTIC. International Journal of Number Theory, 2012, 08 (06), pp.1557-1568. ⟨10.1142/S1793042112500959⟩. ⟨hal-03417874⟩